What is (7+5i)/(1-4i) ?

The solution to (7+5i)/(1-4i) is -13/17+33/17 i

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simplify (7+5i)/(1-4i)

simplify

\frac{7 + 5 i}{1 - 4 i}

- \frac{13}{17} + \frac{33}{17} i

Solution steps

\frac{7 + 5 i}{1 - 4 i}

Multiply by the conjugate

\frac{1 + 4 i}{1 + 4 i}

= \frac{( 7 + 5 i ) ( 1 + 4 i )}{( 1 - 4 i ) ( 1 + 4 i )}

Simplify

\frac{( 7 + 5 i ) ( 1 + 4 i )}{( 1 - 4 i ) ( 1 + 4 i )} : \frac{- 13 + 33 i}{17}

= \frac{- 13 + 33 i}{17}

Rewrite in standard complex form:

- \frac{13}{17} + \frac{33}{17} i

= - \frac{13}{17} + \frac{33}{17} i

- \frac{5}{4} + 2

- x^{2} + 2 x + 48

- 8 \frac{\frac{1}{7}}{- 5} \frac{5}{9}

81 - - 4

6 m^{2} n^{2} - 3 mn + 14 mn + 10 m^{2} n^{2} + 9